Which of the statements given below is true with respect to India's Third Five-Year Plan?
I. It was named the 'Gadgil Yojana' after the Deputy Chairman of the Planning Commission.
II. A core objective was to achieve economic self-reliance and transition into a self-generating growth phase.

The correct option is Both I and II.

Let us analyze both statements step-by-step with respect to India's Third Five-Year Plan (1961–1966):

1. Statement I Analysis:
Statement I is true. The Third Five-Year Plan was commonly known as the 'Gadgil Yojana'. It was named after Dr. D. R. Gadgil (Dhananjay Ramchandra Gadgil), a prominent social scientist and economist who served as the Deputy Chairman of the Planning Commission. His strategic ideas and formula for financial resource allocation heavily guided the framework of the plan.

2. Statement II Analysis:
Statement II is true. The primary objective of the Third Five-Year Plan was to make the Indian economy self-reliant and transition it into a self-generating growth phase. To achieve this, the plan focused extensively on attaining self-sufficiency in food grains through agricultural development while simultaneously expanding basic and capital goods industries to decrease dependence on foreign aid and imports.

Therefore, both Statement I and Statement II are correct.